While I agree that wight has not always implied (or even meant) "undead," its usage does suggest something more than just "man" or "person." In my opinion, "wight" evokes ideas such as "dweller," "denizen,' "soul," and/or "spirit" ... those subtle states of being that purely physical descriptions seem to miss.

Its usage prior to Tolkien, to me, is along the lines of "soul" as in the phrase "she is a kind soul" rather than "she is a kind person;" the first phrase isn't speaking of an actual soul, but it is saying more about the state of being than the second phrase. As such, and in this sense, it is pretty clear why Tolkien chose the word to name whatever it was that was "living" in the Barrows.

Now as for "wright," that's an entirely different word. Though similar, according to the smattering of etymological research I've done, they are completely unrelated -- they are not derived from each other nor do they share a common source. However I admit I didn't delve deeply into the origin of either word.